What is $ \nabla_{\theta_{k-1}} \theta_{k}$ in the context of MAML?
$\nabla_{\theta_{k-1}} \theta_k$ is gradient of $\theta_k$ with respect to $\theta_{k-1}$, it follows chain rule as noted in the side comment in the image. $\nabla_{\theta} \mathcal L(\theta_k)$ is also not a Hessian but a gradient vector.